NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 366

Line 1 Line 2

1
2

1
2

v even v even

Even Mode

1

3

1
2

1
2

v odd v odd

1

Odd Mode 3

Total
(launch voltage)

1
2

1
2

( v even + v odd ) = 1 ( v even + v odd ) = 0

Voltage launched
onto port 1

Voltage launched
onto port 3

Figure 9-16 Modal decomposition of launch voltages when port 1 is driving as shown
in Figure 9-15.

V

R 1 2 R

∼

3 4 R

R

1
2

v even

1
2

( v even + v odd ) ≠ 0

1
2

v odd

θ ≠ 180 °

t p, odd t p, even

Figure 9-17 Modal decomposition of voltages at node 4 when port 1 is driving, showing
that the odd- and even-mode components of the signal arrive at different times when the
dielectric media is nonhomogeneous, causing forward crosstalk to be finite.

velocities will differ. Therefore, the odd and even components of the signal will
arrive at node 4 at different times and will no longer be 180 ◦ out of phase.
Consequently, for a nonhomogeneous dielectric, the forward crosstalk will be
finite, as depicted in Figure 9-17. The propagation delay of the mode is calculated
from the modal velocities using equation (4-81):

1
√ L odd C odd

c
√ ε eff,odd

ν p, odd = =

1
√ L even C even

c
√ ε eff,even

ν p, even = =